1 Our Process ElevationArm Tower FrontBack

2 Operational Definition Need two things: –a method of measurement or test –a set of criteria for judgment For example, what are operational definitions for the following: –on-time delivery –good service –50% wool blanket source: Moen, Nolan and Provost, Improving Quality Through Planned Experimentation

3 Data Collection Collect 5 data points for each team member Plot run chart (use chart wizard) Construct a histogram (Data | Data Analysis | Histogram) Construct a box and whiskers plot (use box&whiskers.xls) Calculate x-bar and s (Data | Data Analysis | Descriptive Statistics) Discuss results and be prepared to brief results to other groups

4 Data | Data Analysis Descriptive StatisticsHistogram

5 Box and Whiskers XLS Insert | Line Chart

6 What the Exercise Statistics Reveal The sample mean (x-bar) describes typical distances in one number. Other measures of central tendency include: median and mode. The sample standard deviation (s) provides a measure of the ‘average’ deviation around the mean.

7 Using x-bar and s The empirical rule assumes the underlying distribution is normal: – 68% within ± 1 s – 95% within ± 2 s – 99 % within ±3 s For any distribution: – At least 75% within ± 2 s – At least 89% within ± 3 s

8 Histograms Shows the distribution of process outcomes. Look for center, shape and spread Compare to: –your expectations and knowledge –target and specification requirements –across shifts, operators, machines, etc

9 Process capability EXCEL: =Normdist(x, mean, std dev, 1) to calculate percent non-conforming material.

10 Process capability measure Estimate standard deviation: Look at standard deviation relative to specification limits Don’t confuse control limits with specification limits: a process can be out of control, yet be incapable  ˆ = R / d 2 33 Upper Specification Limit (USL) Lower Specification Limit (LSL) X-3  A X-2  A X-1  A X X+1  A X+2  X+3  A X-6  B X X+6  B Process A (with st. dev  A ) Process B (with st. dev  B ) x  C p P{defect}ppm 1  ,000 2  ,500 3  ,700 4   ,6 6  2.002x ,00 The Statistical Meaning of Six Sigma

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